U.S. patent number 4,692,910 [Application Number 06/711,115] was granted by the patent office on 1987-09-08 for methods of determining lithological characteristics of an underground formation which utilize compressional velocity and shear velocity data.
This patent grant is currently assigned to Amoco Corporation. Invention is credited to Albert L. Frisillo, Janice O. Norris, Carl H. Sondergeld.
United States Patent |
4,692,910 |
Sondergeld , et al. |
September 8, 1987 |
Methods of determining lithological characteristics of an
underground formation which utilize compressional velocity and
shear velocity data
Abstract
Methods and related apparatus are described for determining
lithological characteristics, such as formation material type and
porosity, of an underground formation by utilizing compressional
velocity (V.sub.p) and shear velocity (V.sub.s) data. One described
method utilizes the plotting of V.sub.p and/or V.sub.s versus a
Seismic Parameter, such ad K/.rho. or the Bulk Velocity, and
boundaries of velocity values of certain formation material types
to define a field of data points. By comparing the position of the
data points to the boundaries of the formation material types, the
formation material type and, later, porosity can be determined. A
method is described for determining the presence of a hydrocarbon
gas at a particular location in an underground formation utilizing
the above methods. Also, a method is described for determining
V.sub.s from V.sub.p data and obtained ratios of V.sub.p and
V.sub.s for at least one formation material type.
Inventors: |
Sondergeld; Carl H. (Broken
Arrow, OK), Frisillo; Albert L. (Broken Arrow, OK),
Norris; Janice O. (Tulsa, OK) |
Assignee: |
Amoco Corporation (Chicago,
IL)
|
Family
ID: |
24856830 |
Appl.
No.: |
06/711,115 |
Filed: |
March 11, 1985 |
Current U.S.
Class: |
367/75; 702/13;
702/18 |
Current CPC
Class: |
G01V
1/303 (20130101); G01V 1/284 (20130101) |
Current International
Class: |
G01V
1/30 (20060101); G01V 1/28 (20060101); G01V
001/28 () |
Field of
Search: |
;367/75,38,31,59,63
;364/421,422 |
References Cited
[Referenced By]
U.S. Patent Documents
|
|
|
4373197 |
February 1983 |
Gassaway et al. |
4375090 |
February 1983 |
Thompson et al. |
|
Other References
McCormack et al., "A Care Study of Stratigraphic . . . "
Geophysics, vol. 49, #5. .
Nations, J. F., "Lithology and Porosity from Acoustic Shear and
Compressional . . . " 15 Annual Logging Symposium of SPWLA, 6/2/74
Tencs. .
Eastwood et al. "Basis for Interpretation of Vp/Vs Ratios in
Complex Lithologies," SPWLA 24th Logging Symp., 6/27/83..
|
Primary Examiner: Tarcza; Thomas H.
Assistant Examiner: Lobo; Ian J.
Attorney, Agent or Firm: Brown; Scott H. Hook; Fred E.
Claims
What is claimed is:
1. A method of determining the formation material type at a
particular location in an underground formation by utilizing
compressional velocity data (V.sub.p) and shear velocity data
(V.sub.s), comprising:
(a) calculating bulk velocity (V.sub.B) utilizing V.sub.p and
V.sub.s data wherein ##EQU2## (b) plotting V.sub.B on one axis and
V.sub.p on a second axis to define a field of data points, wherein
each data point corresponds to a particular location in the
underground formation;
(c) including velocity boundaries of V.sub.B and V.sub.p within the
plot of (b) for at least one formation material type; and
(d) determining from the position of a data point relative to the
velocity boundaries, the formation material type.
2. The method of claim 1 wherein the velocity boundaries are
determined in (c) for carbonates, sandstones, and shales.
3. A method of determining the porosity of an underground formation
by utilizing compressional velocity (V.sub.p) and shear velocity
data (V.sub.s), comprising:
(a) calculating bulk velocity (V.sub.B) utilizing V.sub.p and
V.sub.s data wherein ##EQU3## (b) plotting V.sub.B on one axis and
(V.sub.p, V.sub.s or 1/V.sub.s) on a second axis to define a field
of data points, wherein each data point corresponds to a particular
location within the underground formation;
(c) including velocity boundaries of V.sub.B and (V.sub.p, V.sub.s
or 1/V.sub.s) within the plot of (b) for at least one formation
material type;
(d) determining from the position of the data points relative to
the velocity boundaries the formation material types;
(e) including on a third axis in the plot of (b), porosity
boundaries for the formation material types to define a
three-dimensional field of data points;
(f) fitting to the three-dimensional field of data points of (e) a
mathematical surface defined as .phi.=K.sub.1 (V.sub.p, V.sub.s or
1/V.sub.s)+K.sub.2 V.sub.B +K.sub.3, where K.sub.1, K.sub.2 and
K.sub.3 are fitted constants; and
(g) utilizing the V.sub.p and V.sub.s data, solving the equation of
(f) to determine the porosity of the underground formation.
4. A method of determining the presence of a gaseous hydrocarbon at
a particular location in an underground formation by utilizing
compressional velocity data (V.sub.p) and shear velocity data
(V.sub.s), comprising:
(a) determining a first series of porosity values utilizing the
equation Porosity .phi.=K.sub.1 (V.sub.p /V.sub.s)+K.sub.2 V.sub.s
+K.sub.3, where K.sub.1, K.sub.2 and K.sub.3 are fitted
constants;
(b) determining a second series of porosity values utilizing the
equation Porosity (.phi.)=K.sub.4 bulk velocity V.sub.B +K.sub.5
V.sub.p +K.sub.6 where K.sub.4, K.sub.5 and K.sub.6 are fitted
constants and ##EQU4## (c) determining at which location in an
underground formation a value of porosity from (a) is equal to or
less than a corresponding value of porosity from (b) thereby
indicating the presence of a gaseous hydrocarbon.
5. The method of claim 4 wherein step (c) includes utilizing
parallel line plots of the first and second series of porosity
values.
6. The method of claim 4 wherein step (a) comprises:
(a) plotting V.sub.p /V.sub.s on one axis and (V.sub.p, V.sub.s, or
1/V.sub.s) on a second axis to define a field of data points,
wherein each data point corresponds to a particular location within
the underground formation;
(b) including velocity boundaries of V.sub.p /V.sub.s and (V.sub.p,
V.sub.s or 1/V.sub.s) within the plot of (a) for at least one
formation material type;
(c) determining from the position of the data points relative to
the velocity boundaries the formation material types;
(d) including on a third axis in the plot of (a), porosity
boundaries for the formation material types to define a
three-dimensional field of data points;
(e) fitting to the three-dimensional field of data points of (d) a
mathematical surface defined as Porosity (.phi.)=K.sub.1 (V.sub.p,
V.sub.s, or 1/V.sub.s) +K.sub.2 (V.sub.p /V.sub.s)+K.sub.3, where
K.sub.1, K.sub.2, and K.sub.3 are fitted constants; and
(f) utilizing the V.sub.p and V.sub.s data, solving the equation in
(e) to determine the porosity.
7. The method of claim 4 wherein (e) comprises:
(a) plotting S on one axis and (V.sub.p, V.sub.s or 1/V.sub.s) on a
second axis to define a field of data points, wherein each data
point corresponds to a particular location within the underground
formation;
(b) including velocity boundaries of V.sub.B and (V.sub.p, V.sub.s,
or 1/V.sub.s) within the plot of (a) for at least one formation
material type;
(c) determining from the position of the data points relative to
the velocity boundaries the formation material types;
(d) including on a third axis in the plot of (a), porosity
boundaries for the formation material types to define a
three-dimensional field of data points;
(e) fitting to the three-dimensional field of data points of (d) a
mathematical surface defined as Porosity (.phi.)=K.sub.1 (V.sub.p,
V.sub.s, or 1/V.sub.s)+K.sub.2 V.sub.B +K.sub.3, where K.sub.1,
K.sub.2, and K.sub.3 are fitted constants; and
(f) utilizing the V.sub.p and V.sub.s data, solving the equation in
(e) to determine the porosity.
8. A method of determining shear velosity (V.sub.s) comprising:
(a) determining the ratios of V.sub.p and V.sub.s for at least one
formation material;
(b) plotting V.sub.s on one axis and V.sub.p on a second axis for
at least two samples of at least one formation material type to
define a field of data points;
(c) fitting an equation: V.sub.s =K.sub.1 (V.sub.p)+K.sub.2
V.sub.p.sup.2 +K.sub.3 to the field of data points, where K.sub.1,
K.sub.2 and K.sub.3 are fittend constants; and
(d) utilizing the V.sub.p data, solving the equation in (c) for
V.sub.s.
Description
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to methods of determining
lithological characteristics of an underground formation and, more
particularly, to such methods which utilize compressional velocity
(V.sub.p) and shear velocity (V.sub.s) data.
2. Setting of the Invention
In locating, drilling for, and the production of hydrocarbons from
underground formations it is often useful to know certain
lithological characteristics of the underground formations.
Lithological characteristics include the pore and crack porosity,
matrix mineralogy, cementation, permeability, and fluid saturation
of an underground formation. Many methods and related apparatus
have been used for this purpose with the more common methods
including examining core samples from the underground formations,
examining the drill cuttings when drilling a wellbore, and
utilizing various logging procedures after a wellbore has been
established. One disadvantage of these methods is that they all
require the drilling of a wellbore, which is an expensive
undertaking, or the use of a preexisting wellbore. These
measurements also require suitable sample sizes to be recovered,
which is often difficult to achieve. Further, permeability cannot
be determined from rock fragments.
One method used to determine certain lithological characteristics
does not require the use of a wellbore but uses both compressional
velocity (V.sub.p) data and shear velocity (V.sub.s) obtained from
any commercially available manner, as is well known in the
geophysical art. In this method, a plot is made (by hand or with
the aid of a computer) of the rate of compressional velocity
data/shear velocity data (V.sub.p /V.sub.s) on one axis and either
the compressional velocity data (V.sub.p) or the shear velocity
data (V.sub.s) on a second axis. It has been found that different
formation material types have predictable ranges, i.e., maximum and
minimum theoretical values, of V.sub.p and V.sub.s, thus a plot of
data points (corresponding to a particular location or depth point
in the underground formation) can be made. By using previously
obtained data, different areas or boundaries of V.sub.p /V.sub.s or
V.sub.p and V.sub.s data can be placed within the plot for each of
the desired different formation material types. FIG. 1 represents
such a plot and includes typical boundaries for three common
formation material types. The data points which fall within a
particular boundary can usually be categorized as being of the
particular labeled formation material type. This plotting method is
described fully in "Basis for Interpretation of V.sub.p /V.sub.s
Ratios in Complex Lithologies," by Raymond Eastwood and John P.
Castanga, 24th Annual Logging Symposium, SPWLA, June 27-30, 1983,
which is herein incorporated by reference.
A major problem with using the previously described plotting
method, is that the ratio of V.sub.p /V.sub.s is not monotonically
dependent upon porosity regardless of saturation. Specifically,
there can exist natural situations where conditions of saturation
and crack and pore porosity can cause the ratio to exceed the
theoretical maximum value for the uncracked matrix material; this
leads to an ambiguous interpretation of the data plotted in such a
manner.
There is a need for a method of determining lithological
characteristics from compressional and shear data which is easy to
interpret and more accurate.
Two methods described in U.S. Pat. Nos. 4,373,197 and 4,375,090 use
compressional velocity data and shear velocity data to determine
certain mineralogical data; however, these methods are not useful
for the determination of lithological characteristics. To
differentiate between mineralogical characteristics and
lithological characteristics, mineralogy shall be defined as the
study of minerals, i.e., naturally occurring homogeneous phases,
such as gold, iron, calcite, etc. Lithology shall be defined as the
study of combinations of minerals. The methods of these two patents
contain no determinant factors for porosity, fluid saturation, or
crack porosity. Further, these methods cannot be used to determine
the presence of shales in an underground formation because there is
no known "single crystal property" of clays, as is specifically
needed in these methods.
One of the main lithological characteristics that is desirable to
utilize is the underground formation's porosity. Many methods have
been used to determine formation porosity, but most of these
methods require using a wellbore to obtain core samples, or to
operate porosity measuring logging tools. One method used to
estimate the porosity of an underground formation without
necessarily using a wellbore is to use obtained compressional
velocity data in the Wylie Time Average equation, or the Raymer, et
al. equation. The Wylie Time Average method of estimating porosity
has been found to be accurate for porosities below about 10
percent; however, for porosities above about 10 percent, the
porosity prediction using this method is suspect. Another problem
in utilizing either of these methods is that a knowledge of the
matrix velocity and fluid velocity for the particular geographical
area is required. The matrix velocity and the fluid velocity can
only be guessed at before the actual formation material is
analyzed; therefore, the porosity predictions are dependent upon an
operator's "educated guess" or prior experience in a particular
geological environment. Also, both of these use only V.sub.p data.
Since V.sub.s is much more sensitive to crack porosity and displays
a porosity dependence which is different than V.sub.p, it can be
used to provide a more accurate measure of total porosity.
There is a need for a method to determine the porosity of an
underground formation which uses compressional velocity data and
shear velocity data, and which does not require the knowledge of
the matrix velocity and the fluid velocity for that particular
geographical area.
Another lithological characteristic that is desired to be known is
fluid saturation. In reviewing porosity data obtained from
commercially available source, it is known to plot the porosity
measurement from a neutron logging tool as a function of depth
side-by-side with porosity measurements from compensated formation
density information. Wherever the two plot lines cross over each
other this can be an indication that the formation material at that
depth is not fully water or brine saturated, i.e., there can be
gaseous hydrocarbons present. This method of indicating the
presence of gaseous hydrocarbons is usually accurate; however, it
requires the existence of a wellbore to obtain the porosity
measurement(s) from a logging tool. There is a need for a method to
determine fluid saturation without the need of a well-bore.
In the determination of lithological characteristics, as described
above, both compressional velocity data and shear velocity data can
be utilized; however, shear velocity data is not always obtainable.
One known method to obtain an estimate of shear velocity data is to
use compressional velocity data and an estimated Poisson's Ratio.
For example, a Poisson solid has a value of .nu.=0.25 and for such
materials one can compute V.sub.s from a knowledge of V.sub.p.
However, since the deviations from a norm are being sought, i.e.,
hydrocarbon filled versus brine filled reservoir rock, one cannot
presume to know the in situ Poisson's ratio for the brine case
without extensive testing or experience. There is a need for a
simple method of accurately determining shear velocity data that
can be used in the field to determine if shear velocity seismic
lines are to be run, and how best to design the field equipment to
image the desired objectives.
SUMMARY OF THE INVENTION
The present invention is contemplated to overcome the foregoing
disadvantages and meet the above described needs. The present
invention provides a method of determining certain lithological
characteristics of an underground formation by utilizing
compressional velocity data and shear velocity data. In one
embodiment of the present invention, a seismic parameter, such as
V.sub.B or K/.rho., is calculated utilizing previously obtained
compressional velocity data and the shear velocity data. The
seismic parameter is then plotted on one axis and the compressional
velocity (V.sub.p) is plotted on a second axis to define a field of
data points, wherein each data point corresponds to a particular
location in the underground formation. Thereafter, velocity
boundaries, i.e., ranges of maximum and minimum theoretical values,
are determined within the plot for at least one formation material
type, such as sandstone, carbonates, and/or shales, and from the
position of the data points relative to the velocity boundaries, at
least one of the following lithological characteristics can be
determined: formation material type and/or porosity.
Another embodiment of the present invention provides a method for
determining the porosity of an underground formation utilizing
compressional velocity and shear velocity data. Another embodiment
of the present invention provides a method of determining the
presence of a hydrocarbon gas at a particular location in an
underground formation which utilizes compressional velocity and
shear velocity data. Also, another embodiment of the present
invention provides a method of determining shear velocity data from
compressional velocity data.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a lithological discrimination cross plot with
lithological boundaries shown. Influences of porosity (.phi.) and
gas saturation (S.sub.g) on these boundaries are also
indicated.
FIG. 2 is a test of lithological discrimination utilizing
laboratory measurements on carbonates and sandstones.
FIG. 3 is a lithological discrimination cross plot of measurements
of V.sub.p and V.sub.s derived from full wavetrain sonic logs in
three wells.
FIG. 4 is a plot of the theoretical dependence of V.sub.p /V.sub.s
on saturation (.xi.) and crack density (.epsilon.) assuming an
intrinsic Poisson Ratio of 0.25.
FIG. 5 is a plot of the theoretical dependence of a seismic
parameter K/.rho. on saturation (.xi.) and crack density
(.epsilon.) assuming an intrinsic Poisson Ratio of 0.25.
FIG. 6 is a lithological discrimination cross plot of the data of
FIG. 2.
FIG. 7 is a lithological discrimination cross plot of the data of
FIG. 3.
FIG. 8 is a schematic representation of a projection of V.sub.p or
V.sub.s data, V.sub.p /V.sub.s or K/.rho. data, and porosity data
onto a two-dimensional plane.
FIG. 9 is a plot comparison of the Wylie Time Average estimation of
porosity (black) and the Raymer, et al. estimation of porosity
(blue) with K/.rho. (left) and V.sub.p /V.sub.s (right) estimations
of porosity.
FIG. 10 is a plot comparison of porosity estimations of V.sub.p
/V.sub.s and K/.rho. with porosity predictions with Neutron and FDC
logs.
FIG. 11 is a plot comparison of porosity estimations of V.sub.p
/V.sub.s and K/.rho. with porosity predictions from laboratory
measurements from recovered core samples.
FIG. 12 is a plot comparison of porosity estimations of V.sub.p
/V.sub.s and K/.rho. in a wellbore traversing known zones of
gaseous hydrocarbons.
FIG. 13 is a plot of the relative sensitivity of V.sub.p /V.sub.s
and K/.rho. to changes in saturation.
FIG. 14 is a plot of V.sub.p /V.sub.s and K/.rho. as a function of
gas saturation observed in consolidated Berea sandstone and an
unconsolidated Ottawa sand.
FIG. 15 is a plot comparison of V.sub.s from methods of the present
invention (green) and full wavetrain measurement of V.sub.s
(black). The red line is a measure of P-wave transit time.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
The present invention provides a method of determining certain
lithological characteristics of an underground formation by
utilizing compressional velocity and shear velocity data. In this
method either the Bulk Velocity (V.sub.B)=(V.sub.p.sup.2 -
(4/3)V.sub.s.sup.2).sup.1/2 or K/.rho.=V.sub.p.sup.2
-(4/3)V.sub.s.sup.2 is plotted on one axis and either V.sub.p or
V.sub.s is plotted on a second axis. Inverses of V.sub.p or V.sub.s
can be utilized; however, V.sub.p, is preferred because it provides
the best definition of lithological boundaries and yields a tight
pattern of data points. Each of the data points so plotted
corresponds to a particular location within an underground
formation, and can include longitudinal, latitudinal, and depth
components.
The various boundaries of the maximum and minimum theoretical
values of the V.sub.p and V.sub.s data, so plotted, for at least
one formation material type, usually at least carbonates,
sandstones, and/or shales, is placed over the plot. Thereafter, the
relative position of each data point to the boundaries can indicate
what formation material type is present at a particular location in
the underground formation and/or its porosity.
As used throughout this discussion "velocity" data is referred to
but this term can include "slowness" (1/velocity) and "transit
times".
To fully explain the advantages of the above-described method to
previous methods, the following discussion is provided. As
previously stated, one approach that has been used to determine
certain lithological characteristics is to plot the ratio of
compressional velocity to shear velocity (V.sub.p /V.sub.s) on one
axis and shear velocity (V.sub.s) on a second axis, as shown in
FIG. 1. Accepting these boundaries in FIG. 1 as being totally
accurate could lead to errors. For example, a V.sub.p /V.sub.s
value of 1.7 has often been used to define a boundary between
carbonates and sandstones. However, as shown in FIG. 2, laboratory
measurements of values of V.sub.p and V.sub.s for carbonates
(0-symbols) and sandstones (X-symbols) are not confined to the
lithological boundaries indicated in FIG. 1. Instead, both the
sandstones and the carbonates extend far into the area that should
be indicative of shales. The actual lithological characteristics of
these particular materials are known independently and none are
considered to be shaly. Thus, the plot of this combination of
velocity parameters is of limited practicality in interpreting
field data.
Also, examination of FIG. 3, which is a plot of V.sub.p /V.sub.s
versus V.sub.s from velocity data obtained from full wavetrain and
sonic logs from three wells, shows that there is no apparent
discrete lithological separation of the data points and the bulk of
the data suggests that the data points are primarily
limy-sandstones, which definitely is not the case as determined by
log analysis and core samples. This problem of scattering of the
data and incorrect results when using V.sub.p /V.sub.s versus
1/V.sub.s has been investigated and it has been determined that the
problem is the sensitivity of the ratio of V.sub.p /V.sub.s to
crack densities. To illustrate this point, a V.sub.p /V.sub.s
response is plotted in FIG. 4 with the vertical axis as the V.sub.p
/V.sub.s ratio normalized to its uncracked, zero porosity, value
and the X-axis being the crack density, .epsilon.; i.e., the number
of cracks per unit volume. A family of curves is plotted with each
representing the behavior of the ratio at a constant saturation,
where .xi.=1 represents 100% water saturation while .xi.=0
represents 0% water saturation. Note that the plot of the ratio of
V.sub.p /V.sub.s can, at a constant crack density, either be larger
or smaller than its initial uncracked value. This is believed to be
responsible for the undesired scatter of the data points displayed
in FIG. 2 and FIG. 3.
The inventors hereof have determined that a ratio of the Bulk
Velocity (V.sub.B) or K.sub..rho. can be used in place of V.sub.p
/V.sub.s in these plots to accurately determine certain
lithological characteristics of an underground formation. The Bulk
Velocity is equal to (V.sub.p.sup.2 -(4/3)V.sub.s.sup.2).sup.1/2
and K/.rho. is equal to (V.sub.p.sup.2 -(4/3)V.sub.s.sup.2).
Using the same formulations as for FIG. 4, the normalized change in
K/.rho. as a function of saturation .xi. and crack density
.epsilon. is shown in FIG. 5. It is very apparent that K/.rho. does
not exceed the uncracked value of 1. Also apparent in comparing
FIGS. 4 and 5 is that the magnitude of the change in K/.rho.
compared to V.sub.p /V.sub.s for a given saturation change is
larger, which aids in interpretation.
Taking the data used to plot FIG. 2, a seismic parameter (S) is
calculated and plotted versus V.sub.p in FIG. 6. The seismic
parameter (S) as used hereinafter can be either the Bulk Velocity
(V.sub.B) or K/.rho.. Two observations are present in viewing FIG.
6, one is that the data scatter is greatly reduced from that of
FIGS. 2 or 3 and that the entire data set can be defined as a
simple curve or trend. The boundaries chosen for sandstone and
carbonates in FIG. 6 were set by plotting the maximum values
attainable for pure quartz: V.sub.p =19,847 ft/sec and
K/.rho.=153.9.times.10.sup.6 ft.sup.2 /sec.sup.2, and pure calcite:
V.sub.p =21,422 ft/sec and K/.rho.=296.9.times.10.sup.6 ft.sup.2
/sec.sup.2.
The data used to generate the plot of FIG. 3 was replotted using
K/.rho. in FIG. 7. Although the data point distribution shown in
FIG. 7 is more diffused than similar laboratory data would indicate
(due to greater lithological variations in the field data), a
simple trend is again easily defined. Various data points have been
randomly chosen and the predicted formation material type were
compared with core sample data and gamma ray logging results from
the same intervals. It was found that the predictions made using
the method of the present invention agreed very favorably with the
laboratory data and the gamma ray logs.
The means used to carry out this embodiment of the present
invention has not been found to be critical in that many sources of
the velocity data can be used and many different calculation means
can be used. The compressional velocity data and the shear velocity
data can be obtained from conventional seismic methods and
apparatus, as are well-known in the art, and the velocity boundary
data can be obtained from laboratory data, core samples, textbook
values, or any other accurate source. The calculation means can be
as simple as a hand-held calculator or as complex as a programmable
digital computer. Because of the large number of data points used,
it is unlikely that the plots would be made by hand, but can be. An
analog or digital computer-driven plotting device is preferably
used to generate the plots used in the present invention.
The inventors of the present invention have investigated whether or
not the above described method for determining formation material
types could be used to determine the porosity of the formation
material. The inventors discovered that porosity boundaries could
be added on a third axis to the plot described previously to obtain
an accurate estimate of porosity. In this method, the seismic
parameter (S) is calculated using V.sub.p and V.sub.s, as described
above, and the velocity boundaries for at least one formation
material type are determined, also as described above. In addition,
from laboratory data, core samples, textbooks, or the like, certain
maximum and minimum values of porosity are determined for each of
the chosen formation material types.
The seismic parameter (S) is then plotted on one axis and V.sub.p,
V.sub.s, or 1/V.sub.s is plotted on a second axis. From the
position of each data point to the velocity boundaries, one can
determine the formation material type. The third axis (porosity) is
added for each of the formation material types and thus a
three-dimensional range of data points can be made. The inventors
found that the three-dimensional plot of data can generally be
described as planar and thus can be defined in mathematical terms.
Using curve fitting techniques, such as least squares or any other
known mathematical technique, an equation defined as
Porosity(.phi.)=K.sub.1 V.sub.p +K.sub.2 K/.rho.+K.sub.3 is fitted
to the three-dimensional plot, with K.sub.1, K.sub.2, and K.sub.3
being fitted constants. Once the equation has been defined, the
porosity of a formation material is mathematically determined by
using the compressional velocity and shear velocity data for that
particular location in the underground formation.
The method of the present invention has been compared to field data
for accuracy by comparing the porosity predictions of the present
invention, using sonic wavetrain derived values of V.sub.p and
V.sub.s, to those inferred from neutron logs. The porosity
predictions of the present invention compared very favorably.
To explain the present method in detail, FIG. 8 is provided and
schematically represents the method of the present invention to
determine the formation porosity by searching for correlations
among two elastic variables and porosity. Recalling the previous
discussions of V.sub.p /V.sub.s and K/.rho., the inventors found
that the lithological units are ascribed a finite areal extent. The
areal extent is in part a manifestation of the influence of
porosity upon the measured elastic property. FIG. 8 illustrates how
the two-dimensional relations, V.sub.p /V.sub.s and V.sub.s, can be
projected on a three-dimensional surface. The simplest surface, a
plane, is illustrated; however, other multicurved surfaces can be
used and fitted to determine porosity. However, over a certain
range of porosity, the surfaces can be adequately described by a
simple plane. Also, as indicated in FIG. 8, these surfaces may be
lithologically dependent. It is clear from FIG. 8 that the two
lithologies, sandstone and carbonates, can be described by two
different planes and that the plane of the limestone data plunges
more deeply with respect to the Z-axis (porosity) than the plane
fitted to the sandstone data. The difference in the plunge is
significant in that this indicates better porosity resolution of
sandstones than of carbonates, such as limestone, given the
combination of variables plotted. Thus, the inventors hereof have
found a way to use two empirical functions to predict porosity of a
formation material type given compressional velocity and shear
velocity data.
A comparison of the Wylie Time Average Equation, Raymer, et al.
equations and values from the present invention, using actual field
data, is shown in FIG. 9.
The Wylie Time Average Equation is defined as: ##EQU1## where
V.sub.m is the matrix grain velocity, V.sub.f is the fluid
velocity, and V is the P-wave velocity for brine saturated rock.
The matrix grain velocity is an empirical velocity appropriate for
the particular host formation material and, in some cases, has no
intrinsic relation to the velocities of the minerals present or the
velocity of the uncracked or zero porosity host formation
material.
The Raymer, et al. equation is defined as:
The variables are the same as for the Wylie Time Average Equation.
A matrix velocity of 17,850 ft/sec and a fluid velocity of 5000
ft/sec were used in the above given equations with V.sub.p values
to produce the curves plotted in FIG. 9. On the left, the
predictions of porosity from the Wylie Time Average Equation
(black) and Raymer, et al. (blue) are compared to the porosity
predictions of the above described present invention utilizing
K/.rho. (green) as the seismic parameter (S). On the right, the
Wylie Time Average (black) and Raymer, et al. (blue) porosity
predictions are compared to the porosity predictions of the present
invention (red) using V.sub.s and V.sub.p values (obtained from a
sonic wavetrain form) as the seismic parameter (S). The empirically
predicted porosities bracket the Wiley and Raymer, et al.
porosities with the K/.rho. equation predicting a greater porosity
than the V.sub.p /V.sub.s equation predicted.
The porosity predictions based on K/.rho. (red line) and V.sub.p
/V.sub.s versus 1/V.sub.s (green line) are replotted in FIG. 10
with a neutron and a compensated formation density (FDC) porosity
log indicated in black and blue, respectively. The logging tool
porosity predictions appear to agree quite well with the
empirically predicted values of the present invention. The neutron
log (black line), agrees very well with predictions based on
K/.rho.. The FDC log is in better agreement with the V.sub.p
/V.sub.s porosity estimate. As a further test of the porosity
predictions of the present invention, the inventors compared the
K/.rho. and V.sub.p /V.sub.s predictions to porosity measurements
made from actual cores over the same depth internal. The core
porosity is shown in FIG. 11 with the core measurements (crosses)
bounded by the K/.rho. and V.sub.p /V.sub.s predictions, with the
K/.rho. prediction being consistently larger and the V.sub.p
/V.sub.s consistently smaller. Along this depth interval, the two
curves remain separated with the green to the left and the red to
the right. The separation has been observed consistently in
examination from data from other wells. Please note that the lines
cross over each other at depths where gas production in this
particular well is expected. This phenomenon will be described
below.
The porosity predictions from a well are shown in FIG. 12 with the
K/.rho. porosity predictions shown in green and V.sub.p /V.sub.s
predictions shown in red. Note that unlike the curves from FIG. 11,
these porosity predictions overlap and cross each other over nearly
the entire depth interval because gas was detected in this well
over this interval. The inventors hereof believe that the method of
the present invention provides an accurate indication of gaseous
hydrocarbons because V.sub.p /V.sub.s data and K/.rho. data display
different sensitivities to partial saturations (FIGS. 4 and 5). The
inventors calculated the percent change in each parameter for a
saturation change of 100% and plotted these values as a function of
crack porosity in FIG. 13. As anticipated, the change in K/.rho. is
greater than that in V.sub.p /V.sub.s at any porosity value chosen.
These theoretical assessments are substantiated by laboratory
measurements presented in FIG. 14 wherein the normalized values of
K/.rho. and V.sub.p /V.sub.s are plotted as a function of brine or
gas saturation. The normalization factors were taken to be measured
values for each parameter for a 100% brine saturation. Measurements
are presented for a consolidated Berea sandstone and unconsolidated
Ottawa sand. At any level of saturation, the measured change in
K/.rho. exceeds that measured V.sub.p /V.sub.s for any formation
material type. The absolute differences are greater in the
unconsolidated sand. The overlap of the prediction curves of FIG.
13 can therefore be interpreted for the reflection of the partial
saturation condition. The K/.rho. curves cross over to lower
porosity values under such conditions, thereby indicating the
possible presence of a gaseous hydrocarbon.
The inventors hereof have found a method of determining the
presence of a hydrocarbon gas at a particular location in an
underground formation by determining a first series of porosity
values using V.sub.p /V.sub.s, as described above, and determining
a second series of porosity values using K/.rho. or V.sub.B, as
described above. Wherever the porosity value using V.sub.p /V.sub.s
is equal to or greater than a corresponding porosity value using
K/.rho. or V.sub.B, gaseous hydrocarbons can be present.
The means used for calculating and plotting the porosity values of
the present invention can be the same as described earlier,
including the use of a programmable digital computer to be used in
the following manner:
input boundaries of V.sub.p and V.sub.s for at least one formation
material type;
input boundaries of porosity for the chosen formation material
type(s);
calculate the porosity values in with the above described method;
and
compare such porosity values and output the depths where gaseous
hydrocarbons are predicted.
Another method of the present invention is the determination of a
shear velocity estimation from V.sub.p data and known values of
V.sub.p and V.sub.s for different formation material types. An
additional consequence of the K/.rho. plot in FIG. 6 is that the
data can be fit to a single function, a line or curve, regardless
of formation material types. This is important because this
empirical function can then be used with V.sub.p information to
predict V.sub.s data. This need for V.sub.s data arises in
situations where only P-wave data exists and an estimate of
shear-wave data is required before seismic lines are to be run.
In the method of the present invention, a plot is made of a
function of V.sub.p on one axis and a function of V.sub.s on a
second axis for at least two samples of at least one formation
material type. A larger number of samples improves the definition
of the formation material type and more formation material types
improve the predictive capability of this method. Once the plot is
made, then an equation in the form of V.sub.s =K.sub.1 V.sub.p
+K.sub.2 V.sub.p.sup.2 +K.sub.3, where K.sub.1, K.sub.2, and
K.sub.3 are fitted constants, is fitted to the plot of the data
points. Once the equation has been determined, one can simply take
an obtained V.sub.p value and solve the above equation for V.sub.s
to obtain an estimate of V.sub.s.
For example, a least squares fit to the data plot of FIG. 6 yields
the following equation:
This fit is based entirely on laboratory measurements from both
carbonate and sandstone cores taken from the field where the
V.sub.p and V.sub.s data of FIG. 6 was obtained. The measurements
were taken from those made at confining pressures in excess of 3000
psi pressure under brine saturated conditions. Clearly, downhole
conditions of undersaturation would cause deviations from certain
predictions and the inventors have compared the above to sonic
wavetrain derived V.sub.p velocity data to compare the predicted
shear wave velocity with that measured by the same tool. These
comparisons are shown in FIG. 15 and the information plotted is
from two different wells. The red curve in FIG. 15 represents the
measured P-wave transit time and the black and green curves are the
measured and predicted shear wave transit time. When the same type
of comparison is made between predicted and measured shear-wave
velocities in other wells, the V.sub.s disagreement is usually less
than .+-.5%, which is completely acceptable.
As previously shown and described above, the inventors hereof have
found novel combinations of utilizing lithological information,
compressional velocity data and shear velocity data to (a)
determine formation material type in an underground formation, (b)
determine the porosity of an underground formation, (c) determine
the presence of a hydrocarbon gas at a particular location in an
underground formation, and (d) determine shear velocity from
obtained compressional velocity data and ratios of V.sub.p /V.sub.s
for at least one formation material type.
Wherein, the present invention has been described in particular
relation to the above discussion and drawings attached hereto, it
should be understood that other and further modifications, apart
from those shown or suggested herein, may be made within the scope
and spirit of the present invention.
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